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   "source": [
    "# 过拟合与欠拟合\n",
    "本篇讨论一个机器学习中最基本的理论，过拟合与欠拟合，力图用最直白的语言来阐述。    \n",
    "`` Tips: 深度学习是机器学习的子集，机器学习又是人工智能化的子集。    \n",
    "本篇会重点讨论什么是过拟合和欠拟合，具体表现，解决方法，以及结合多项式拟合给出具体的实验结果。\n",
    "\n",
    "## 1. 训练集、测试集、验证集\n",
    "任何一个机器学习任务，我们都需要收集许多样本，比如在企业中经常要处理的CTR预估模型，用户没有点击过的是负样本，用户点击过的是正样本（不过实际中常常用随机的方法选择正样本），然后我们学习得到我们的模型，但是模型一定是应用到我们没有见过的样本上面的，这些样本就是测试集。实际中在机器学习过程中不可能看到测试样本，所以我们常常通过一种方法来模拟出测试样本，也就是验证集。通常，我们将样本分成N分，拿其中N-1份当做训练集，剩余一份当做测试集，然后求N份分别当测试集的效果的平均值，来模拟我们在真实情况下的误差。这种方法称为N择交叉验证法。最后将模型应用的线上，观测实际效果。\n",
    "\n",
    "注意：后文说的测试集都是验证测试集合，是从训练样本中取出一部分的集合，欠拟合和过拟合都指的是训练集和验证测试集上的表现。如果验证集表现不错，但实际线上效果很差，这个很有可能是样本构造或者特征处理没有对齐，后面专门讲解如何处理此类情况。\n",
    "\n",
    "## 2. 过拟合和欠拟合通俗理解\n",
    "### 2.1 过拟合\n",
    "+ 具体表现：模型在训练集的误差远远好过在测试集上的表现\n",
    "+ 解决方法：常见的方法有，正则化、DropOut、增加训练样本、选择复杂度更低的模型、提前终止学习\n",
    "\n",
    "### 2.2 欠拟合\n",
    "+ 具体表现：模型在训练集的误差很高\n",
    "+ 解决方法：常见的方法有，选择复杂度更高的模型、增加学习次数\n",
    "\n",
    "## 3. 实际案例讲解\n",
    "下面结合多项式拟合的案例来说明过拟合和迁拟合的具体表现，已经解决的方法。首先需要生成模拟样本。我们假定训练样本和测试样本均是按如下公式生成：y=1.2x-3.4x^2+5.6x^3+5+sigma，其中sigma是服从均值为0，方差为0.01的正态分布。暂时先假设训练样本和测试样本的数量都是100。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "n_tain = 100\n",
    "n_test = 100\n",
    "feature = torch.randn(200, 1)\n",
    "# 按列组合在一起\n",
    "true_x = torch.cat((feature, torch.pow(feature, 2), torch.pow(feature, 3)), 1)\n",
    "true_y = 1.2*feature - 3.4*torch.pow(feature, 2) + 5.6*torch.pow(feature, 3) + 5 + torch.tensor(np.random.normal(0.0, 0.01, size=(200, 1)), dtype=torch.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[ 1.0176,  1.0355,  1.0538],\n        [-0.4359,  0.1900, -0.0829]])\ntensor([[8.6013],\n        [3.3800]])\n"
    }
   ],
   "source": [
    "print(true_x[0:2])\n",
    "print(true_y[:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 模型定义\n",
    "本篇继续利用 Pytorch Lighting 来定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import torch\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "from torch.nn import functional as F\n",
    "from torch.utils.data import DataLoader\n",
    "from torch.utils.data import TensorDataset\n",
    "import pytorch_lightning as pl\n",
    "import numpy as np\n",
    "\n",
    "class PolyModel(pl.LightningModule):\n",
    "\n",
    "    def __init__(self, linear_layer, traind, testd):\n",
    "        super(PolyModel, self).__init__()\n",
    "        self.l1 = linear_layer\n",
    "        self.epoch_valid_loss = []\n",
    "        self.epoch_train_loss = []\n",
    "        self.traind = traind\n",
    "        self.testd = testd\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.l1(x)\n",
    "\n",
    "    def training_step(self, batch, batch_idx):\n",
    "        # 必须提供：定于训练过程\n",
    "        x, y = batch\n",
    "        y_hat = self.forward(x)\n",
    "        loss = F.mse_loss(y_hat, y)\n",
    "        tensorboard_logs = {'train_loss': loss}\n",
    "        return {'loss': loss, 'log': tensorboard_logs}\n",
    "\n",
    "    def training_epoch_end(self, outputs):\n",
    "        # 结束一轮训练，自测一下\n",
    "        x, y = iter(self.traind).next()\n",
    "        y_hat = self.forward(x)\n",
    "        train_loss = F.mse_loss(y_hat, y)\n",
    "        self.epoch_train_loss.append(train_loss.item())\n",
    "        tensorboard_logs = {'train_loss': train_loss}\n",
    "        return {'loss': train_loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def validation_step(self, batch, batch_idx):\n",
    "        # 可选提供：定义测试过程\n",
    "        x, y = batch\n",
    "        y_hat = self.forward(x)\n",
    "        loss = F.mse_loss(y_hat, y)\n",
    "        tensorboard_logs = {'valid_loss': loss}\n",
    "        return {'val_loss': loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def validation_epoch_end(self, outputs):\n",
    "        # 可选提供：定义验证过程，验证集上效果，每轮都会验证\n",
    "        avg_val_loss = torch.stack([x['val_loss'] for x in outputs]).mean()\n",
    "        self.epoch_valid_loss.append(avg_val_loss.item())\n",
    "        tensorboard_logs = {'valid_loss': avg_val_loss}\n",
    "        return {'val_loss': avg_val_loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def configure_optimizers(self):\n",
    "        # 必须提供：定义优化器\n",
    "        # can return multiple optimizers and learning_rate schedulers\n",
    "        # (LBFGS it is automatically supported, no need for closure function)\n",
    "        return torch.optim.SGD(self.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        # 必须提供：提供训练数据集\n",
    "        return self.traind\n",
    "\n",
    "    def val_dataloader(self):\n",
    "        # 可选提供：提供测试数据集\n",
    "        return self.testd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "GPU available: False, used: False\nTPU available: False, using: 0 TPU cores\n\n  | Name | Type   | Params\n--------------------------------\n0 | l1   | Linear | 4     \n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "# 训练集用全部数据，模型拟合3次函数\n",
    "train_dataloader = DataLoader(TensorDataset(true_x[:100], true_y[:100]), batch_size=10, shuffle=True, num_workers=0)\n",
    "test_dataloader = DataLoader(TensorDataset(true_x[100:], true_y[100:]), batch_size=100, shuffle=False, num_workers=0)\n",
    "poly_model = PolyModel(torch.nn.Linear(3, 1), train_dataloader, test_dataloader)\n",
    "trainer = pl.Trainer(logger=False, max_epochs=50, num_sanity_val_steps=0, progress_bar_refresh_rate=0)\n",
    "trainer.fit(poly_model)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Parameter containing:\ntensor([[ 1.2876, -3.3654,  5.5698]], requires_grad=True)\nParameter containing:\ntensor([4.9590], requires_grad=True)\n"
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 打印所有参数 y=1.2x-3.4x^2+5.6x^3+5+sigma\n",
    "for i in poly_model.parameters():\n",
    "    print(i)\n",
    "import matplotlib.pyplot as plt  \n",
    "def plot_epoch_loss(train_loss_list, test_loss_list):\n",
    "    x_vals = list(range(len(train_loss_list)))\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('loss')\n",
    "    plt.plot(x_vals, train_loss_list, 'g--',label='train_loss')\n",
    "    plt.plot(x_vals, test_loss_list, 'r--',label='valid_loss')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "plot_epoch_loss(poly_model.epoch_train_loss, poly_model.epoch_valid_loss)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "可以看出训练集误差和验证测试集误差均越来越小，最终都靠近0，模型很好的学到了训练集的特征，并且成功应用到验证测试集，也保持通用好的效果。\n",
    "\n",
    "### 3.2 用简单模型拟合复杂模型-模拟欠拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "GPU available: False, used: False\nTPU available: False, using: 0 TPU cores\n\n  | Name | Type   | Params\n--------------------------------\n0 | l1   | Linear | 2     \n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 训练集用全部数据，模型拟合1次函数\n",
    "train_dataloader = DataLoader(TensorDataset(feature[:100], true_y[:100]), batch_size=10, shuffle=True, num_workers=0)\n",
    "test_dataloader = DataLoader(TensorDataset(feature[100:], true_y[100:]), batch_size=100, shuffle=False, num_workers=0)\n",
    "poly_model2 = PolyModel(torch.nn.Linear(1, 1), train_dataloader, test_dataloader)\n",
    "trainer = pl.Trainer(max_epochs=50, num_sanity_val_steps=0, progress_bar_refresh_rate=0)\n",
    "trainer.fit(poly_model2)\n",
    "plot_epoch_loss(poly_model2.epoch_train_loss, poly_model2.epoch_valid_loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出训练集误差和验证测试集误差都一直比较大，模型没法从数据中根本学不到东西。一般发生欠拟合，我们通常通过下面的手段去解决：\n",
    "+ 增加训练迭代次数\n",
    "+ 增加模型复杂度\n",
    "\n",
    "### 3.3 用少量样本训练模型-模拟过拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "GPU available: False, used: False\nTPU available: False, using: 0 TPU cores\n\n  | Name | Type   | Params\n--------------------------------\n0 | l1   | Linear | 4     \n"
    },
    {
     "output_type": "display_data",
     "data": {
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/oMCHvltugf33h+OO84u2l5VFt48iIiIistdISUlh06ZNPyuoSBXnHJs2bSLlJ15dF9GlFySGNWjgl2xYuRIefhgeeghOOQWefRZOPRXKy/2yDiIiIiJSb+Xk5LBq1Sry8vKi3ZV9XkpKCjk5OT/pnDpZeiFScnNz3ezZs3/8QIm88nJ46y0YOhRSU+HWW+Hpp2H8eDjzTGjePNo9FBERERGJOVFfekHqgYQEOOEEH/QA2rf3C7Nffjm0agUnnQQvvxzVLoqIiIiI1CcKexIZY8fCrFnw1VdwxRUwezY88EBV/dtv/SQvIiIiIiISEQp7EllduvhLOr//Hh591LetXAmdOkGPHn45h3XrottHEREREZEYpLAndSMhAVq08PuNGsF990FGBvzud5CT4y8B/eabqHZRRERERCSWKOxJ3cvMhPPPhxkzYNEi+P3v4csv/QyfAB9+CP/5D5SWRrefIiIiIiL7MIU9ia6DDoKbb4blyyE727fdeaef0KVlS79g+3vvQUVFVLspIiIiIrKvUdiTvYNZ1f4zz8Brr/kF3J991i/nEFzMXUREREREdotWvZa9T1KSD3fHHw+FhfD6674NYPt2GDAATjwRTj8dunePbl9FRERERPZSGtmTvVtaGowZAyNG+Od5edC6Nfz97342z27d4KabNKOniIiIiMgPKOzJvqV9e3jrLVizBu69F5o0gT/+ETZs8PVFi/zaflrDT0RERETqOYU92Tc1bw4XXggffQSrV1ddznnLLX60r3NnuPZamDNHwU9ERERE6iWFPdn3tWpVNcHL3/7mR/xycvylnrm5MGhQdPsnIiIiIhIFmqBFYkt2th/xu/BC2LTJr9cXXLahosKHv/794ZRTYPBgSEyMandFRERERCJFI3sSu5o2hfHjYcIE/3zLFjjwQHj8cTjmGL+O37nnwty5UeykiIiIiEhkKOxJ/dG0Kbzwgp/Rc+pUGD7cPwYnd/n6a3j4Yc3sKSIiIiIxQZdxSv2TlgYjR/qttBTi43371Knwhz/4/YMPhhNO8FuvXuGLvouIiIiI7AM0sif1W1JSVdi79lqYN8+v22cG11/vJ3cpLfX1b7+FoqLo9VVERERE5CdQ2BMJMvMLtV93HXz6KaxdCy+/DMnJvj5qFDRr5hd4f+ghXxcRERER2Usp7InUpkULGDrU7zsH//hH1YQuv/61X/Lh97+vOr6yMirdFBERERHZGYU9kd1hBsceC3ffDcuXw/z58Ne/wpFH+vp330FWFpx2Gjz6KKxZE9XuioiIiIhoghaRn8oMunf3W1B5OZx4IkybBs8959u6d4d//xv69IlKN0VERESkfovYyJ6ZpZjZLDObZ2ZfmdmfA+3tzWymmS0xs+fMLCnQnhx4viRQbxepvonscR06+GC3Zo2/zPPWW/1IX06Orz/wABx/PNx5J3zzjb8sVEREREQkgiJ5GWcJMMQ51xPoBQwzs/7ArcDtzrkDgXwgsOI1E4D8QPvtgeNE9i1m0LOnv5dv+nRo3ryqtmQJXHIJdOoE7dvDRRcp9ImIiIhIxEQs7Dlve+BpYmBzwBBgSqD9MWBkYH9E4DmB+lAzLW4mMWLiRD+it2wZ3Hcf9O7t94Nf8YsvhmuugXfegcLC6PZVRERERGJCRCdoMbN4M5sLbADeAZYCW5xz5YFDVgGtA/utgZUAgfpWoOlOXnOimc02s9l5eXmR7L7Inte+PVxwgV/A/a23fJtzsGiRn+3zmGOgUSM44gh46qmodlVERERE9m0RDXvOuQrnXC8gBzgY6LQHXvMB51yucy43Kyvrl76cSPSZwbvvQn4+vPkmXHop7NgBq1b5+pYtcNxx8Pe/w+zZUFERzd6KiIiIyD6iTmbjdM5tMbP3gQFAIzNLCIze5QCrA4etBtoAq8wsAWgIbKqL/onsFTIyYNgwv0HV/XwrV8L338NVV/nnjRrB4MFwww3+/kARERERkZ2I5GycWWbWKLCfChwNLATeB0YHDhsHvBLYfzXwnED9Pec0e4XUY8H7+bp3h6++8jN9PvUUjBoF8+ZBQuB3NVOnwimnwO23w5w5fhkIEREREan3Ijmylw08Zmbx+FD5vHPuNTP7GnjWzG4CvgAeDhz/MPCEmS0BNgOnRbBvIvue7Gw44wy/QdXI39atPvxNneqfZ2TAYYf556mp/jjNdSQiIiJS79i+PHiWm5vrZs+eHe1uiOwdVq+Gjz/227Jl/v4/gLPPhhUrYNAgvw0YAJmZ0e2riIiIiOwRZjbHOZe7s1pEJ2gRkTrUujWcdhrcc09V0AO/rl9xMdxyCxx7LDRuDOecU1XPz6/7voqIiIhIxNXJBC0iEkXXXee37dthxgw/8teiha+Vl0NOjl/8fcCAqq1nT0hMjG6/RUREROQX0WWcIvVZYSHcf78Pgf/7n58EBuDPf4Y//QkKCuC993wAbN48un0VERERkRp2dRmnRvZE6rO0NLj8cr/vnF/mYcYM6NHDt82YASNH+v0DDqga+Rs1qmp0UERERET2Sgp7IuKZQdu2fgsaNMhf9jljht/eeQeefBL69/dh7913Ydo06NfPb+3aaeZPERERkb2Ewp6I1C4lBQ4/3G/gR/+WL4c2bfzzefPgrrugpMQ/b9bMh74pU/yoYWkpJCVFpesiIiIi9Z1m4xSR3WcG7dtXLeh+xRWwbRvMng333Qcnnuhn/kxL8/Vx42C//WD0aPj73+H99/3xIiIiIhJxGtkTkV8mKQn69vXbBReE14491o8GzpoFL77o23r3hs8/9/vPP+8vB+3VCxo2rNNui4iIiMQ6hT0RiZzx4/0GsHGjHwEsL/fPKyvhV7/yM34CHHigD4Jjx/qRQBERERH5RRT2RKRuNGsGw4ZVPY+Lg2+/hS++8CN9X3zhw+BBB/mwV1AAXbv6Ub8+fXwQ7NPHrwuoSWBEREREfpTCnohET8uWcNxxfguqrPSPBQV+NtDPP4fXX69qv/9+OP98WLfOzw7asyd06qSJYERERER+QGFPRPYucYF5o1q18ss8AOzYAfPn+9G/IUN82yefwDnn+P2EBOjc2a8PeP310KGDv1w0Pl6jgCIiIlJvKeyJyN4vPb1qQfegkSPhq698CAxuH33kAx7APffATTf5ANijhx8BDO4n6K8+ERERiX36H4+I7JsSEqBLF7+ddlrNerduPhDOmweTJ0NRkR/lKyjw5z75JCxe7O8L7NoVOnaExMQ6/xgiIiIikaKwJyKxaehQvwFUVMDSpT7cpaf7tg8/hEceqboXMCHBjxx+9JF/PmsWZGb6WUIVAkVERGQfZM65aPfhZ8vNzXWzZ8+OdjdEZF9VVATffAMLFvhLQs3g5pt9rWdPf2loYqKfIbRrVzjqKL9cBPgAGbxkVERERCRKzGyOcy53ZzWN7IlI/ZWa6pd26NWrZu3xx33Y++orv82c6Uf/gmGvdWto1MjPBBrcDjnETxQjIiIishdQ2BMR2ZmePf1WXfCSz/JyH/oWLYKFC+GNN6CsDK68Ev7+dygshOHDw4Ngp07Qtm3VbKMiIiIiEaawJyKyu4JBLSHBz/QZVF4O330HKSn++ebNvu2FF/x+0J13wm9+A6tWwb33+iUiOnb0j1lZWiZCRERE9iiFPRGRXyohwQe2oJwcvw4gwMaNfvRv0SIYONC3ffst/N//+UAY1KABvPwyHHmkn0zm00/9a3boAI0b19lHERERkdihsCciEknNmvmQFwx64BeGLyqC5cv9DKGLF/sA2K6dr7/9Nlx0UfhrdOgATz/tj1m6FPLy4IADfE0jgiIiIrITCnsiItGQkOCXdTjwQDjuuPDaeefB4ME+AFYPg8ERvkceqZo1NDPTh7799/drB6am+ktKnfP3CGoBeRERkXpL/wsQEdnbJCf7WT1rm9nzggv8moBLl/pt2TI/Shi8Z/D66+GJJ3zQ228/Hwa7dIHbb/f1FSsgIwOaNNGooIiISAyLWNgzszbA40ALwAEPOOfuMLMbgF8DeYFDr3XOvRE45xpgAlAB/NY5Ny1S/RMR2We1aeO32lx6qR8ZDIbBpUv9IvFB48fDBx/4wNe+vb80tH9/uPZaX1+6FJo29UtLiIiIyD4rkiN75cAVzrnPzSwTmGNm7wRqtzvn/lH9YDPrApwGdAVaAe+aWUfnXEUE+ygiEnv69PFbba69FkaM8Jd7Ll/uH6tf7nnssT7wNWrkg2C7dr7tggt8/csvoWVL3S8oIiKyl4tY2HPOrQXWBvYLzGwh0HoXp4wAnnXOlQDfmdkS4GBgRqT6KCJSLx19tN9q889/+vsEly/327ff+hlGwd8L2K8flJT4+wPbtvXb6afDuef6+gcf+LacHH9JqoiIiERFndyzZ2btgN7ATOAw4GIzOweYjR/9y8cHwU+rnbaKnYRDM5sITARo27ZtZDsuIlIfjRhRe62yEp59Fr7/3t/79/33fguuJ7hxo59tNKhlSx/8rrgCxo6F7dv9IvQ5OX7LzobExMh+HhERkXoq4mHPzDKAF4FLnXPbzOw+4C/4+/j+AvwTOG93X8859wDwAEBubq7b8z0WEZFaxcfDyJG11zMzYfr0qhAY3IIL0n/7LZx6atXxcXE+EN5zj3/d77+H556rCoM5OdC6NSQlRfJTiYiIxKSIhj0zS8QHvaeccy8BOOfWV6s/CLwWeLoaqD7jQE6gTURE9hUpKeEjez/UtSvMnw+rVoVvwctE582D3/++5nnTp/vXnTHDLz3RqpUPga1a+a1Ll6rZSEVERASI7GycBjwMLHTO3VatPTtwPx/AycCCwP6rwNNmdht+gpYOQLXp40REZJ+XnAzdu/ttZ048EbZuDQ+CK1dCx46+/v338J//wIYN/v7AoK++8oHv8cf9KGH1IJid7UcT09KguNiPEgZHGkVERGJYJEf2DgPOBr40s7mBtmuB082sF/4yzuXA+QDOua/M7Hnga/xMnpM0E6eISD3UoIEPbl261Kydeqrfyspg/XpYswZWr/ZLSIAPdA0b+stFP/gA8vN9+6hR/vH66/0ENC1a+MtHs7P94+TJ/hLV+fOhoKCqPS2tTj6yiIhIJJhz++5tb7m5uW727NnR7oaIiOytCgth7VrYf3+/TMS77/oQuHYtrFvnt+3b4Ztv/PFnnglPP111foMG0KkTzJzpnz/8sB9tbNGiamvVyi9PISIiEgVmNsc5l7vTmsKeiIhIwOLFfo3BYBBcu9Zf8nn77b5+wgnw+uvh53Tv7kcEAcaM8ZedBoNg8+a+HpyUZvFiv5h9s2aahVRERPaIXYW9Oll6QUREZJ/QoYPfavPaa1BaCnl5/jLS9evD7/9r187fc7h8uR8NzMuDY46pCntHHeXvOwS/aH1WFpxyCtxyi2/729/8paNZWVVbTo4PhyIiIj+Rwp6IiMhPkZTkJ4BpXWMpWPi//wt/XlEBRUVVz++8099nmJfntw0bqoKcc3DjjX4SmeouvBDuvRfKy30QbdrUn9Osmd8//ngfKMvK4OOPw2ta1F5EpF5T2BMREYmU+Hh/2WbQrhasN4MdO/ykMsEguHGjX5QeoKQEBg3ybRs3wpIl/rF5cx/21q2DoUPDXzM9Hf7xD7jgAn+v4eWXQ5MmPgg2ber3jzjCT3BTUuJHJZs0gQT990BEJBbob3MREZG9RVxcVRDr1Cm8lp4Ojz1W85zgvffNmsH77/sAuGmTD4ybN1fNarp1K3z5pa9t3uxHHQGeesqHvU8/hcGDfVuDBj70NW4Md9wBAwf65S0ef9y3BWuNG0O/fn4G1PJy338tayEistdQ2BMREdmXmfnH1NSqsLYzXbvCwoV+v7LSLzGxaZMPluBnLL3rLh8EN23yI4z5+T5kgl/O4l//8vcsVjdjBvTvD08+Ceed5+9FDAbBRo3goYf8vYz/+x+8955vq7716+cvNy0v9yOhwc8jIiK/mMKeiIhIfRMX50fjGjasamvTBi6+uPZzTj7Z309YVFQVBPPzfYgE6NED/vCHqvYtW/xjcNbRTz6BP/6x5uuuX+8vRb3xRj9BTaNGVX1r2NDPfpqaCq+8AnPmhNcaNvSXsAJs2+bDYlqaAqOISIDCnoiIiOweMx+m0tJqTlDTp4/favP738Oll/rLSbdsqdqaNPH1QYP86F6wfds2vwUnmZk+He6+u+qyVfD92LHD7190kb8kNSHBX4baoAHst59fVxHgttv8eooNGkBmpn9s1QrGjvX1RYv8iGdmZtUWH/8LflgiItGndfZERERk31BZCdu3+8C4dSsUFsLBB/vam2/69Q63bvWXqG7bBikpMHmyr48fD9Om+fbCQt/WrZu/jxHg0EP9JanVDRwIH33k9087zc+kWj0M9u7tQybAs89WhcWMDL+1aFE1wU55uSa+EZGI0KLqIiIiIkHl5T4QlpRAy5a+7eOPfZjbts3XCgp8WLvgAl8//3w/MhisFRT40cjnnvP17Gw/I2p1p57qQyD4S05LSqqCYEaGD5B/+IMfrRw3zo9UpqdXbYce6gNneTm8/bY/J1jLyPCjomlpdfMzE5G9lhZVFxEREQlKSPATyFQ3cOCuzwmOENbm8899UNy+vWrLyqqqX311VZAM1oOT45SV+QlsCgr8ZanBS1Ovvtr3a+tWv57iD/3lLz4srlwJ3bv7EBgMjGlpcMUVMGoUrF4N119f1R48ZtgwP1trfj7MnFlVS031jy1b+n3ndB+kyD5KYU9ERETkl8rO9lttrrmm9lpSkl83Mcg5PxFOUIMG/hLTYBAMbsF7JFNS4Jxz/OWphYW+VlhYddlofr6/zDXYXlbm21u08GHvyy/huONq9mvqVBg50p87cmR4EExL8zOtHnKIn3zn9tt9rfr2m99ATg58/TX8979V5wbrBx/sn2/Z4oNuaqr/LKmpul9SZA9R2BMRERHZmwQnwglKTPTLW9QmKwvuvLP2erdufnQvqKzMh77g5De9evkwVlTk24OPwTDZvr0fJQy2B7eMDF/fssVf4ho8N7idfroPex98AJMm1ezXt99Chw7w4IN+Ap/qEhL8iGXLlj5I3n9/VRAMPr70kn989ln48EPfXn37/e/9z/J//4MVK8Jr6elV93tu2OCXFElJ8T+T5GT/M9dopsQA3bMnIiIiIpFTWOjXb6weBIuK/KhgaqofWZw507cVF1ct8fGHP/jQ+/zzfpSxer242I8oJiT44x58sKq9tNSPlpaU+PcfNw4efzy8T02a+PUkwV/q+tJL4fX99oPly/3+6af7MBwMgsnJ0LmzX1sS/KjtsmX+PYP1Dh387LPg+7Z1q28PHtO2LQwZ4usffwwVFVW1pCTfv+CMt5s2+fCZlOS3uLg9+acjMUATtIiIiIhI/VBZWTVSB37kLj8/PCg6B4MH+/r06bB0qQ+HwS09vSqs3XabD6TBWnGxD2v33efrZ5zh79ksLa06JjcX3nrL1zt18iOf1R13HLzxht/PyQkfeQUYM8aHXPBrT27dWlVLSIAJE/xoJ/hgGh/vg2AwFJ51Flx2me/LyJFVQTF4zMiRftu+3a9xGTwvMdFvgwdDv37+PtOXXgqvJSb6dTXbtPGXBi9YEF5LTPSXCGdk+FHkHTvCaxox3eM0QYuIiIiI1A9xcVVBD6B5c7/VZuhQv9Xm8st3/X5PP73r+vz5VSEwGAiTkqrqU6f60FVaWrVVv//zllv86Gjw/NLSqktsnYOjjvKhqvr5wUtsy8v9yGBpafgx3bv7ekEB3HWXr1VUVL3nP/7hw96aNXDuuTU/0+TJMHEiLFy480uMn3rKh+D//heOPDK8Fh8PL78MJ5zgl0M5+2wfYBMTqx4fe8yP/L79Ntxwg2+vfswdd8CBB/qg/uijNet//KP/M//4Y/8ewfbgdv75/mc0ezbMnRtei4/3QTgx0a+/+f33VbXc3H1uBlyFPRERERGRSAmOqGVm7rzer9+uzw8u/7EzZvDww7XX09Nh1qza69nZVZMBVVb60FdW5oMOwAEH+EtUg2ExuO23n68feCC8/np4rawMBgyoOv+222rWDzzQ11u2hNGjfVt5edVj8GeVkOBDWbBWVFR1DPhR208/rWoLbpdd5sPezJnwt7/5z1bdWWf5133lFbjpppo/l+Bo5OTJ8K9/VbUvWgQHHVT7z3MvpMs4RUREREQkdlVW+pHL4AhmerofAd62zW/Vg2J5uZ+lNi7O37e5erU/p7zcj2LuhSN7uoxTRERERETqp7g4vwVHLIMaNPBbbdq189s+TNP5iIiIiIiIxCCFPRERERERkRiksCciIiIiIhKDFPZERERERERiUMTCnpm1MbP3zexrM/vKzC4JtDcxs3fMbHHgsXGg3czsTjNbYmbzzaxPpPomIiIiIiIS6yI5slcOXOGc6wL0ByaZWRfgamC6c64DMD3wHOA4oENgmwjcF8G+iYiIiIiIxLTdCntmdomZNQiMvj1sZp+b2TG7Osc5t9Y593lgvwBYCLQGRgCPBQ57DBgZ2B8BPO68T4FGZpb90z+SiIiIiIiI7O7I3nnOuW3AMUBj4Gzglt19EzNrB/QGZgItnHNrA6V1QIvAfmtgZbXTVgXaRERERERE5Cfa3bBngcfhwBPOua+qte36RLMM4EXg0kBgDHHOOcDtZh+CrzfRzGab2ey8vLyfcqqIiIiIiEi9sbthb46ZvY0Pe9PMLBOo/LGTzCwRH/Secs69FGheH7w8M/C4IdC+GmhT7fScQFsY59wDzrlc51xuVlbWbnZfRERERESkftndsDcBP5FKP+dcIZAInLurE8zMgIeBhc6526qVXgXGBfbHAa9Uaz8ncF9gf2Brtcs9RURERERE5CdI2M3jBgBznXM7zOwsoA9wx4+ccxj+3r4vzWxuoO1a/L1+z5vZBGAFMDZQewM/crgEKORHwqSIiIiIiIjUbnfD3n1ATzPrCVwBPAQ8DhxR2wnOuU+o/b6+oTs53gGTdrM/IiIiIiIisgu7exlneSCMjQDuds7dA2RGrlsiIiIiIiLyS+zuyF6BmV2DvyxzoJnF4e/bExERERERkb3Q7o7snQqU4NfbW4efKfP/ItYrERERERER+UV2K+wFAt5TQEMzOwEods49HtGeiYiIiIiIyM+2W2HPzMYCs4Ax+NkzZ5rZ6Eh2TERERERERH6+3b1n7zr8GnsbAMwsC3gXmBKpjomIiIiIiMjPt7v37MUFg17App9wroiIiIiIiNSx3R3Ze8vMpgHPBJ6fil8EXURERERERPZCuxX2nHNXmtko4LBA0wPOuamR65aIiIiIiIj8Ers7sodz7kXgxQj2RURERERERPaQXYY9MysA3M5KgHPONYhIr0REREREROQX2WXYc85l1lVHREREREREZM/RjJoiIiIiIiIxSGFPREREREQkBinsiYiIiIiIxCCFPRERERERkRiksCciIiIiIhKDFPZERERERERikMKeiIiIiIhIDFLYExERERERiUEKeyIiIiIiIjFIYU9ERERERCQGKeyJiIiIiIjEIIU9ERERERGRGBSxsGdmj5jZBjNbUK3tBjNbbWZzA9vwarVrzGyJmX1jZsdGql8iIiIiIiL1QSRH9v4NDNtJ++3OuV6B7Q0AM+sCnAZ0DZxzr5nFR7BvIiIiIiIiMS1iYc859xGweTcPHwE865wrcc59BywBDo5U30RERERERGJdNO7Zu9jM5gcu82wcaGsNrKx2zKpAWw1mNtHMZpvZ7Ly8vEj3VUREREREZJ9U12HvPuAAoBewFvjnT30B59wDzrlc51xuVlbWHu6eiIiIiIhIbKjTsOecW++cq3DOVQIPUnWp5mqgTbVDcwJtIiIiIiIi8jPUadgzs+xqT08GgjN1vgqcZmbJZtYe6ADMqsu+iYiIiIiIxJKESL2wmT0DDAaamdkq4HpgsJn1AhywHDgfwDn3lZk9D3wNlAOTnHMVkeqbiIiIiIhIrDPnXLT78LPl5ua62bNnR7sbIiIiIiIiUWFmc5xzuTurRWM2ThEREREREYkwhT0REREREZEYpLAnIiIiIiISgxT2REREREREYpDCnoiIiIiISAxS2BMREREREYlBCnsiIiIiIiIxSGFPREREREQkBinsiYiIiIiIxCCFPRERERERkRiksCciIiIiIhKDFPZERERERERikMKeiIiIiIhIDFLYExERERERiUEKeyIiIiIiIjFIYU9ERERERCQGKeyJiIiIiIjEIIU9ERERERGRGKSwJyIiIiIiEoMU9kRERERERGKQwp6IiIiIiEgMUtgTERERERGJQQp7IiIiIiIiMShiYc/MHjGzDWa2oFpbEzN7x8wWBx4bB9rNzO40syVmNt/M+kSqXyIiIiIiIvVBJEf2/g0M+0Hb1cB051wHYHrgOcBxQIfANhG4L4L9EhERERERiXkRC3vOuY+AzT9oHgE8Fth/DBhZrf1x530KNDKz7Ej1TUREREREJNbV9T17LZxzawP764AWgf3WwMpqx60KtNVgZhPNbLaZzc7Ly4tcT0VERERERPZhUZugxTnnAPczznvAOZfrnMvNysqKQM9ERERERET2fXUd9tYHL88MPG4ItK8G2lQ7LifQJiIiIiIiIj9DXYe9V4Fxgf1xwCvV2s8JzMrZH9ha7XJPERERERER+YkSIvXCZvYMMBhoZmargOuBW4DnzWwCsAIYGzj8DWA4sAQoBM6NVL9ERERERETqg4iFPefc6bWUhu7kWAdMilRfRERERERE6puoTdAiIiIiIiIikaOwJyIiIiIiEoMU9kRERERERGKQwp6IiIiIiEgMUtgTERERERGJQQp7IiIiIiIiMUhhT0REREREJAYp7ImIiIiIiMQghT0REREREZEYpLAnIiIiIiISgxT2REREREREYpDCnoiIiIiISAxS2BMREREREYlBCnsiIiIiIiIxSGFPREREREQkBinsiYiIiIiIxCCFPRERERERkRiksCciIiIiIhKDFPZERERERERikMKeiIiIiIhIDFLYExERERERiUEKeyIiIiIiIjFIYU9ERERERCQGJUTjTc1sOVAAVADlzrlcM2sCPAe0A5YDY51z+dHon4iIiIiIyL4umiN7RzrnejnncgPPrwamO+c6ANMDz0VERERERORn2Jsu4xwBPBbYfwwYGb2uiIiIiIiI7NuiFfYc8LaZzTGziYG2Fs65tYH9dUCL6HRNRERERERk3xeVe/aAw51zq82sOfCOmS2qXnTOOTNzOzsxEA4nArRt2zbyPRUREREREdkHRWVkzzm3OvC4AZgKHAysN7NsgMDjhlrOfcA5l+ucy83KyqqrLouIiIiIiOxT6jzsmVm6mWUG94FjgAXAq8C4wGHjgFfqum8iIiIiIiKxIhqXcbYApppZ8P2fds69ZWafAc+b2QRgBTA2Cn0TERERERGJCXUe9pxzy4CeO2nfBAyt6/6IiIiIiIjEor1p6QURERERERHZQxT2REREREREYpDCnoiIiIiISAxS2BMREREREYlBCnsiIiIiIiIxSGFPREREREQkBkVjnb2YN/r50SzauIjWDVqTk5lD6wat6da8G2O7+qUDC0oKyEjKILDWoIiIiIiIyB6nsBcBfbL7UOEqWL1tNV+u/5J129cxaL9BobB3yEOH8N2W72id2doHwgY5HLHfEUzsOxGAuevm0jilMS0zWpKckBzNjyIiIiIiIvsohb0IuHbgtWHPyyrK2F66PfT8kkMuYcnmJawqWMXqbauZsXIGqQmpobA38NGBoeObpjYlOzObc3qcw5WHXYlzjns+u4cW6S3IzswmOyOb7Mxs0hLT6u4DioiIiIjIXk9hrw4kxifSOLVx6Pn5uefXeqxzjmdHPcva7WtZW7CWtdvXsqZgDelJ6QBsLdnKb978TY3zbjjiBq4ffD1birdw4esX0iK9hd8yWtAyoyU9W/SkdYPWe/7DiYiIiIjIXklhby9jZhzf8fha6w2TG5J3ZR5rCtaEhcHD2x4OwJbiLXy2+jPW71gfNpp47/B7ubDfhcxbN48jHzuSFhlVYbBFegvO630evVr2Ir8on0UbF9E8vTlZ6VlkJmXq3kIRERERkX2Qwt4+xsxoltaMZmnN6NGiR416u0btWPLbJQAUlhWyfvt61u9YT9uGbQHITM7k9G6ns36Hb/9i7Res37Geo/c/ml4tezFj1QyOf7oqbCbFJ5GVlsVzo5/jsLaHMXvNbJ6a/xRZ6VlkpWWRlZ5F8/Tm9GrZS5eSioiIiIjsRRT2YlhaYhrtG7enfeP2obb9G+/PPcffU+NY5xwA/Vr14/UzXidvRx55hXmhx+bpzQH4dtO3PPTFQ2GjhgDzL5hP9xbduX/2/fzp/T/RLK0ZTdOa0jS1Kc3SmnHrUbfSNK0pCzYsYFn+MpqmNqVpmq81TmlMfFx8BH8SIiIiIiL1jwX/k78vys3NdbNnz452N+qlorIiNhZuDAXCgfsNJC0xjfe+e4/nv3qeTUWb2Fi4kU2Fm9hUtIkvL/ySJqlNuHb6tfztk7+FvZZhFFxTQHpSOnd8egdvLnmTJqlNwrZLDrkEM2Pp5qWUVJTQJLUJjVMaa7ZSEREREanXzGyOcy53ZzWN7MnPkpqYSpuGbWjTsE1Y+5D2QxjSfkit510+4HJGdR4VFgY3F20OXQJaVlnG5qLNLM1fyuaizeQX5ZOZnMml/S8F4Lr3ruO5r54LvV5aYhodm3bki/O/AODmj2/mm03f0DilMY1SGtEopRFtGrRhVJdRACzLX0a8xdMopRGZyZnEWdye/LGIiIiIiOw1NLIne7VKV0lBSQENUxoCMGfNHJZsXuKDYHE+m4s2kxSfxM1DbwZgwisTmP7ddPKL89lWsg2Ani16MveCuYBf43DW6lmAH1FsmNKQIe2H8OLYFwH47Zu/Jb84n4bJDf2W0pAuWV04oeMJofdPTkgO1TKSMhQYRURERCRqNLIn+6w4iwsFPYC+rfrSt1XfWo9/eMTDof2Kygq2lWyjuLw41PaXI//Cqm2r2FK8JbQFJ68BWLx5MYs2LmJr8Va2lmyl0lVycqeTQ2Fv2FPD2Fi4MXS8YUzoPYEHT3oQgCMfO5Kk+CQykzJpkNyAzKRMhrQfwohOI6h0lTy74NmqWrJ/bJ7enAbJDX75D0tEREREpBqFPYlZ8XHxYesbAhxzwDG7POfNM98M7Tvn2FG2g/LK8lDbM6OeYXPRZraVbAsFwm7Nu4WOT4pPYlvJNlZtW0VBSQHbSraRnJDMiE4j2FG6gzNfOrPGe/5x0B+58cgb2bBjAwfeeSCZyZlkJGWQmeQfJ/WbxJiuY8jbkcffPvlbqD143ICcARzQ5AAKywpZsnkJ6YnpZCRlkJ6UTlpimkYeRUREROophT2RWpgZGUkZYW1H7X/ULo+fdta0WutpiWksmrSIglIfAoNb9+bdAUiIS+C83uexvXQ7BaUFbC/dzvbS7VS6SgDyCvN48PMHa8yE+vBJD3NAkwOYv34+Ax4eUON9nx/9PGO6juF/K//H+a+dHxYG0xPTufrwq+nRogcL8xby4sIXSUtMIz3RB8X0pHQGtxtMk9QmbC7azPrt60MhMj0xnZSEFK3DKCIiIrKXUtgTqSPxcfEc1OygWutNUpvwr2H/qrXeJasLBdcUUOkqKSwr9KGwpICs9CwAOjTpwItjX2R76XZ2lO5gR9kOtpdup2vzrgCkJKTQoUmHUPvGwo2hfYB56+fxx/f/WON9Z/5qJge3PpiXFr7Er//z6xr1ry/6ms5ZnXnki0e49b+3kpaYRmpCqn9MTOXREY/SLK0Zby15i3eWvhNqT01IJTUxlXN7nUtyQjIL8xayatuqsFpqQirtGrXDzKiorCDO4hQuRURERHaTwp7IPibO4shIyiAjKYOWGS1D7U3TmnJK51NqPa9Pdh9eOvWlWuundTuNUZ1HUVhWyI6yHf6xdAcdmnYA/Eyrz4x6JtS+o2wHRWVFoTUYW6S3oE92HwrLCikqK6KwrJD84nwMH84+X/s5k+dMprCsEEfVxFDn9DwHgMlzJnPHzDvC+mQYFX+qAOCC1y7g4S8eJiUhhdTEVFISUmiW1ox5F8wD4IYPbuCT7z8hJSEltLXMaMk/jvkHAE/Me4IVW1eEasnxyWSlZzGy00gAZq2exY7SHb6WkExKQgoNkhuQ0yAHgMKyQhLiEkiMS1TgFBERkX2Cwp6IhCTGJ9IwvmHYpDhB+zfen/0b71/rucd3PJ7jOx5fa/3agddy7cBrcc5RWlFKYVkhxeXFpCakAnBp/0sZ3WU0RWVFFJUXUVRWRGlFaShYnXjQibTMaElxeTFF5UUUlxeTEFf1V5hzjuLyYrYUb6G4vJji8uLQqCfAk18+ydtL3w7rU9esrqGwd8lbl/Dpqk/D6v1z+jNjwgzAz+S6YMMCDCMpPonkhGSOOeAYXhjzAgDHPHEMeYV5JMcnk5yQTFJ8EoP3G8x1g64D4Ddv/IbSitJQLSk+iX6t+nFy55MBuPeze4m3+LB6x6Yd6dGiB5WukhkrZ5AUn0RifGKo3jS1KY1TG1PpKtleuj3Urvs0RUREBLT0gojUI+WV5T4slhVRUlECEBq5m79+PpuLNlNcXkxJeQnF5cU0SmnEsQceC8DDnz/M2u1rKSkvobSilJKKEjo06cCkgycBcP5/zvf1ipLQMYPbDQ4tC9Lt3m5sLNxISYWvlVaUMq7nOB466SGcc8TfGB824glwySGX8K9h/6KwrJD0m9NrfJ7rBl7HTUNuYsOODbT4R4tQe5zF+SVJhtzMZQMuY8WWFRzx7yNIjE8kMS4x9HjN4dcwqssoluUvY9Ibk0iMSwwFysS4RC7IvYBD2xzKsvxl3DPrHj+yWe01RncZTcemHVmxZQVvLXmLxPjE0OhnYnwig/YbRPP05qzfvp6v874OnZ8Ql0BCXAIdm3YkLTGNgpIC8ovzQ+cG6+lJ6QquIiIiP0JLL4iI4CfBCV4C+0M9WvTY5bkT+kzYZX3yiZN3WV9w0YIabdV/2bbhyg2hEBjcGqf42WST4pN4+6y3KakooayijNKKUsoqy+ia5e/HTEtM4x9H/yPUXlpRSllFGb2zewOQnJDM4HaDQ/WyijLKKstITfSjqqUVpWwq3BRWK6soY1TnUQCsKVjD5DmTKa8sp6yyLDRpUPfm3enYtCPz18/ngtcvqPH53jvnPZq3b857373HGS+dUaP+2a8/I7dVLs8seIbzXzu/Rn3RpEUc1Owgbp9xO79/9/ehEBjc5l8wn+zMbO749A7u/uzuGvUPxn1AelI698++nylfTwmrxcfFM2XMFMyMf8/9Nx+t+Ih4iw/V0xLTuPXoWwF4/qvnWbBhgT/P4omPi6dhckMu7HchAG8sfoOVW1eGXjchLoFGKY1CS7b89/v/kl+cHzo33uJplNIotIzMgg0LKC4vDqtnJmeGloVZW7CWSldJnMWF6skJyaHvcUl5SaimcCwiItXtdSN7ZjYMuAOIBx5yzt1S27Ea2RMRqXuVrpKyirJQuCkpL2FT0SYfBgNhsbyynHaN2pGRlMGGHRv4Ou9ryivLQ1tZRRmD2w2mcWpjvtn4DZ98/0lVLXD+hN4TaJzamE++/4Q3F78Zdn55ZTk3D72ZhikNefHrF3lp0Us16i+OfZGUhBTunnU3zyx4horKilCtwlXw5YVfAnD1u1fz9JdPh9rLK8tJTUhl1eWrADjjxTN4ZsEzYT+DVpmtWH35agCOf/p43lj8Rlj9oKYHsejiRQAMenQQH3//cVg9t1Uun/36MwB6T+7N3HVzw+qD2w3m/XHvA9Dhrg4s2bwkrH5ixxN59fRXAWj5j5as37E+VIu3eM7scSaPjXwMgOx/ZofCZDAUjus5jluOuoVKV0nHuzqGhcV4i2d8r/FcPuBydpTuYOjjQ4mzuLBjzu11Luf0PIeNhRsZ9/K4qnrgPcb3Gs8JHU9gTcEarn736lA9uJ3T8xwOb3s432/9nn/+7581Xv/0bqfTs2VPvsv/jsfmPVbj/DFdxnBAkwNYunkp//n2PzXqJx10Eq0yW7F081I+/v7jULthxFkcww4cRuPUxizLX8bcdXNrnH/EfkeQnpTOii0rWLJ5CWYW9hqH5BxCUnwSq7atYk3BmrDXNjO6N+9OfFw867avI78oP9QefI3gJfGbizZTWFYYOt/MiLf40CXo20u3U15ZHvba8RYf+kVNeWU5zrnQawdfQ0Tql31mZM/M4oF7gKOBVcBnZvaqc+7r6PZMRESC4iyO5ITk0PPkhGRaZbaq9fjm6c1DE/nszEHNDtrlTLWHtz2cw9seXmt9VJdRjOoyqtb6xQdfzMUHX1xr/ZajbuGWo2r9vSJPj3qap0c9TaWr9IGwsiI0ugnw5MlPUlReFAqTFa4ibITtwRMfZFvJNipcBRWVFVS4CtITqy7LvXPYnWwp3hJWb5bWLFS/ecjNNertGrUL1a85/BoKSgtCtYrKirCR6rN7nE1xeXGo3xWuImx90P45/alwgVrgmKapTX0dR6OURqHzKl1laAOoqKxgw44NYedWuko2FW4C/MRGn3z/Sag9+BpH7HcEh7c9nLwdeTw+//Ea5/fN7kvPlj1Zlr+MP3/45xp/Jj1a9OCAJgewYMMCLpt2WY16l6wutMpsxYxVMzj3lXNr1D+f+DmNUxszbck0Lnrjohr1xb9ZzIFNDuS5r57jqnevqlFfd8U6WmS0YPLsydz08U016juu3UFaXBq3fHJLjYmn4iwuNPHUlW9fySNzHwmrN0huwNartwJw3ivn8cLXL4TVW2e2Dv0i4sRnTuStJW+F1Ts168TCSQsBOPKxI/nv9//FzEJBsF+rfnx07kcADHx0IF+u/zIsjA7abxAvjn0RgEMfPpQVW1eEzjWMYw44hodOegjw9zJvKtwUOt8wTjroJP5+9N8ByH0gl5KKktD5waB+7cBrqXSVHPLQIWGvbWac1f0sJh08ie2l2xn+1HCAsPp5vc7j7J5ns7FwI2e8eEaoFjzu/L7nM7LTSFZuXcmkNyaFwm/w/En9JnHU/kexZPMSrpl+Tdj7g798fkCbAXy14Sv+9snfarz+5f0vp2fLnnyx9gvunnV3jde/8tAr6dC0AzNXzeSxeY+F1QzjqsOvIqdBDv/9/r+88PULNT7/1YdfTbO0Znyw/APeWPxG2HsbxnWDriMjKYN3l73Lh8s/DNWC73PdoOtIik9i2pJpzFw9M+z8OIvj2oHXAv6KhHnr5oWdm5KQwiX9LwHgP9/8h282fRN2foPkBvyqz68AeGXRKyzfsjzs/CapTTizh19PeOrCqazdvjbs8zdPbx6aSO6lhS+F/p4IfrZWma04rsNxAEz5egoFJQVhr9+mYRuGtB8CwAtfvUBxeXFYvX3j9hza5lDAX5FRUVkRVj+wyYH0bdUX5xxTvp5S42fXsWlHurfoTllFGa99+1qNeqdmnXb5b9Xeaq8Ke8DBwBLn3DIAM3sWGAEo7ImISFQF74UkPry9cWpjGtO41vN+7D8HA/cbuMv6mK5jdlkP/uesNsH/eO9MfFw8T57yZK31jKQM3jrrrVrrLTJahEYod+bAJgey7JJltdb7tupL/lX5tdaH7j+Uyj9V4nBhQTMxLhGA4R2Gk39VflitorKCJqlNABjZaSTfXfJdWN05x36N9gNgbNexHNb2sBrnB+/lPaP7GQzIGeDPq9aHxqn+z/vsnmczoM2AGq+fHO9/GTKu57jQ+cHXqH5F1fhe48POd86RGJ8YVj+0zaGhWqWrDLsMfVzPcRzW5rBQzeHCflFwerfTq/rvHA4X+mwAJ3U8iT4t+4Q+m3MuNAMzwJHtjmTDjg2hfjtc2C8S+mb3ZWvJ1rDXD15+DNChaQdKyktC51e6ytDl6c45stKywl7bORf2i6SEuISwemVl+C8aCkoLQj/P4HFFZUUAlFWWsXLbytB7BevbSrYB/hcRX234KuzPxOHIL/bfx60lW5mxakaN1x/fczwAG3ZsYNrSaWE1h+O83ufRgQ6s2LqCKV9PCasBTOw7kZwGOSzauIhH5z4a1jeAi/pdRLO0Zny+9nPumnVXWP8BLhtwGRlJGXy04iNu/uTmsP4BXHX4VSTFJ/Hmkjd3+ouGYNh78esXa/yioWFyw9DfJ0/Mf6LGLxpyGuSEwt7kOZN5c8mbYfXOzTqHwt5tn97GJ99/Elbv16pfKOzd+OGNzFs/L6w+pP2QUNi76t2rWJYf/nfHiINGhMLepDcmkVeYF1Y/q8dZobA3/uXxFJUXhdUvzL2Qvq36UukqGTtlLD905aFX8vej/86Osh2c8nzN2c1vHHwjfzyi5hJVe7u96jJOMxsNDHPO/Srw/GzgEOfcxdWOmQhMBGjbtm3fFStWRKWvIiIiIiJ7o2AAh/AwmhSfBEBZRRkVzo8wVw+TaYlpABSXF1NWURZ2fnB0D6CgpICyyrKw8+MsLvSLlvyifMoqy8JeOyEuIfTLiA07NlBWURYWdJMTkkNXgazetjrs9QFSE1NDS04t37Kc8srysHpmcmao/u2mb0O/GAjWG6U0IjszG+ccX+d9HepXsN4srRnZmdlUVFawYMOCGvWWGS3Jzsz+mX8ikbWryzj3ubBXne7ZExERERGR+mxXYW9vm7ZrNdCm2vOcQJuIiIiIiIj8BHtb2PsM6GBm7c0sCTgNeDXKfRIREREREdnn7FUTtDjnys3sYmAa/hb4R5xzX0W5WyIiIiIiIvucvSrsATjn3gDe+NEDRUREREREpFZ722WcIiIiIiIisgco7ImIiIiIiMQghT0REREREZEYpLAnIiIiIiISgxT2REREREREYpDCnoiIiIiISAwy51y0+/CzmVkesCLa/diJZsDGaHdC6g1936Su6LsmdUXfNakr+q5JXYrU920/51zWzgr7dNjbW5nZbOdcbrT7IfWDvm9SV/Rdk7qi75rUFX3XpC5F4/umyzhFRERERERikMKeiIiIiIhIDFLYi4wHot0BqVf0fZO6ou+a1BV916Su6LsmdanOv2+6Z09ERERERCQGaWRPREREREQkBins7WFmNszMvjGzJWZ2dbT7I7HDzB4xsw1mtqBaWxMze8fMFgceG0ezjxIbzKyNmb1vZl+b2VdmdkmgXd832ePMLMXMZpnZvMD37c+B9vZmNjPw7+lzZpYU7b5KbDCzeDP7wsxeCzzXd032ODNbbmZfmtlcM5sdaKvzf0cV9vYgM4sH7gGOA7oAp5tZl+j2SmLIv4FhP2i7GpjunOsATA88F/mlyoErnHNdgP7ApMDfZfq+SSSUAEOccz2BXsAwM+sP3Arc7pw7EMgHJkSvixJjLgEWVnuu75pEypHOuV7Vlluo839HFfb2rIOBJc65Zc65UuBZYESU+yQxwjn3EbD5B80jgMcC+48BI+uyTxKbnHNrnXOfB/YL8P8pao2+bxIBztseeJoY2BwwBJgSaNf3TfYIM8sBjgceCjw39F2TulPn/44q7O1ZrYGV1Z6vCrSJREoL59zawP46oEU0OyOxx8zaAb2Bmej7JhESuKxuLrABeAdYCmxxzpUHDtG/p7Kn/Av4PVAZeN4UfdckMhzwtpnNMbOJgbY6/3c0IdJvICJ1wznnzEzT68oeY2YZwIvApc65bf4X4J6+b7InOecqgF5m1giYCnSKbo8kFpnZCcAG59wcMxsc5e5I7DvcObfazJoD75jZourFuvp3VCN7e9ZqoE215zmBNpFIWW9m2QCBxw1R7o/ECDNLxAe9p5xzLwWa9X2TiHLObQHeBwYAjcws+Etp/Xsqe8JhwElmthx/q80Q4A70XZMIcM6tDjxuwP8S62Ci8O+owt6e9RnQITCrUxJwGvBqlPskse1VYFxgfxzwShT7IjEicA/Lw8BC59xt1Ur6vskeZ2ZZgRE9zCwVOBp/n+j7wOjAYfq+yS/mnLvGOZfjnGuH/z/ae865M9F3TfYwM0s3s8zgPnAMsIAo/DuqRdX3MDMbjr8ePB54xDn31+j2SGKFmT0DDAaaAeuB64GXgeeBtsAKYKxz7oeTuIj8JGZ2OPAx8CVV97Vci79vT9832aPMrAd+ooJ4/C+hn3fO3Whm++NHX5oAXwBnOedKotdTiSWByzh/55w7Qd812dMC36mpgacJwNPOub+aWVPq+N9RhT0REREREZEYpMs4RUREREREYpDCnoiIiIiISAxS2BMREREREYlBCnsiIiIiIiIxSGFPREREREQkBinsiYiIRJCZDTaz16LdDxERqX8U9kRERERERGKQwp6IiAhgZmeZ2Swzm2tmk80s3sy2m9ntZvaVmU03s6zAsb3M7FMzm29mU82scaD9QDN718zmmdnnZnZA4OUzzGyKmS0ys6fMzKL2QUVEpN5Q2BMRkXrPzDoDpwKHOed6ARXAmUA6MNs51xX4ELg+cMrjwFXOuR7Al9XanwLucc71BA4F1gbaewOXAl2A/YHDIvyRRERESIh2B0RERPYCQ4G+wGeBQbdUYANQCTwXOOZJ4CUzawg0cs59GGh/DHjBzDKB1s65qQDOuWKAwOvNcs6tCjyfC7QDPon4pxIRkXpNYU9ERAQMeMw5d01Yo9kff3Cc+5mvX1JtvwL9+ysiInVAl3GKiIjAdGC0mTUHMLMmZrYf/t/J0YFjzgA+cc5tBfLNbGCg/WzgQ+dcAbDKzEYGXiPZzNLq8kOIiIhUp98siohIveec+9rM/gC8bWZxQBkwCdgBHByobcDf1wcwDrg/EOaWAecG2s8GJpvZjYHXGFOHH0NERCSMOfdzr0gRERGJbWa23TmXEe1+iIiI/By6jFNERERERCQGaWRPREREREQkBmlkT0REREREJAYp7ImIiIiIiMQghT0REREREZEYpLAnIiIiIiISgxT2REREREREYpDCnoiIiIiISAz6f69TxLSBU7m4AAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 训练集用2个样本数据，模型拟合3次函数\n",
    "train_dataloader = DataLoader(TensorDataset(true_x[:2], true_y[:2]), batch_size=10, shuffle=True, num_workers=0)\n",
    "test_dataloader = DataLoader(TensorDataset(true_x[100:], true_y[100:]), batch_size=100, shuffle=False, num_workers=0)\n",
    "poly_model3 = PolyModel(torch.nn.Linear(3, 1), train_dataloader, test_dataloader)\n",
    "trainer = pl.Trainer(max_epochs=50, num_sanity_val_steps=0, progress_bar_refresh_rate=0)\n",
    "trainer.fit(poly_model3)\n",
    "plot_epoch_loss(poly_model3.epoch_train_loss, poly_model3.epoch_valid_loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出训练集的误差很快就降到0附近，但是验证测试集的误差一直都很大，模型的泛化性很差。一般出现模型过拟合，我们可以通过以下手段去解决：\n",
    "+ 增加训练样本数量 => 从案例3.1可以看出通过增加训练集数量可以解决过拟合\n",
    "+ 降低模型复杂度 => 实际中一般是通过正则化来达到目的（可以简单就不要追求复杂）\n",
    "\n",
    "在机器学习中，有一个没有免费的午餐定理，也就是说模型没有好坏之分，只有针对某个数据集，有更合适的模型而已\n",
    "  \n",
    "+ 增加正则化 => 主要有L1正则化和L2正则化，本质就是在损失函数中给模型的参数加一个惩罚，使的学到的参数尽可能简单\n",
    "+ 提前停止训练 => early stop，当训练样本下降到一定的误差，并且测试样本误差也下降到一定程度提前终止训练\n",
    "+ dropout => 训练的时候，随机的去掉一些网络中的隐藏层的节点\n",
    "不过正则化和样本数量通常是相互作用的，样本数量越多，正则化效果越差。\n",
    "\n",
    "后面我们会通过过拟合处理章节来系统的学习如何处理过拟合。\n"
   ]
  }
 ]
}